with \({\mathcal {A}} = \sqrt{h^2+\gamma ^2-1}\) , and the \(-(+)\)  signs in the second term of
the second equation above refers to the region \(h>1 (<-1)\) , respectively.
The coefficients of \(\delta ^2\)  in the first terms of the right hand side of the two equations in Eq. (REF )
are the components of the information metric in the \(h-\gamma \)  plane [1]}, [2]}. This is in lines with
the argument given in [3]}, i.e., the infinitesimal NC (with the differential element \(dh\)  identified with \(\delta \) )
gives the line element on the parameter space. The other terms in this equation represent higher order corrections.
Similarly, for a fixed value of the magnetic field \(h\) , writing \(\gamma ^R=\gamma \)  and
\(\gamma ^T=\gamma +\delta \) , we obtain
\({\mathcal {C}}_N\big |_{|h|<1} &=& \frac{\delta ^2}{16 |\gamma | (|\gamma | +1)^2}\mp \frac{(3 |\gamma | +1) \delta ^3}{32 \gamma ^2 (|\gamma | +1)^3}\nonumber \\&+&\frac{(|\gamma | (43 |\gamma | +28)+7) \delta ^4}{384 |\gamma | ^3 (|\gamma | +1)^4} + {\mathcal {O}}(\delta ^5)~,\) 
